By Dr. Robert Finkelstein

References: The Structure of Scientific Revolutions, Thomas Kuhn, Third Edition, 1996Philosophical Foundations Of Physics, Rudolph Carnap, Edited By Martin

Gardner, 1966

Philosophical Foundations of Science And Quantitative Analysis

Section 1: Definitions

Philosophy

Theory of the principles underlying conduct, thought, knowledge, and the nature of the universe

Included are such fields as: logic, epistemology, metaphysics, ethics, and aesthetics

The love of - or search for - wisdom or knowledgeGeneral principles or laws of a field of knowledgeA system of principles for the conduct of life

A study of human morals, character, and behavior

KnowledgeThe act, fact, or state of knowing

Acquaintance or familiarity with a fact or entityAwarenessUnderstanding

All that has been grasped or perceived by the mind

Learning and enlightenmentBody of facts, principles, etc. accumulated by mankindA posteriori knowledge (i.e., “knowledge by acquaintance”)

Knowledge derived from experience (i.e., senses)

A priori knowledge (i.e., “knowledge by description”)

Knowledge independent of experience (e.g., mathematical knowledge) or transmitted from others having sensed experience

EpistemologyThe study or theory of the nature, sources, and limits of knowledge

What is it to know something?What counts as evidence for or against a particular theory?What is meant by a proof?Is human knowledge possible at all?

Analytic propositionsThe meaning of the predicate term is containedin the meaning of the subject termExample: “All husbands are married” (“husband”includes in its meaning “being married”)

Synthetic propositionsThe meaning of the predicate term is notcontained in the meaning of the subject termExample: “All birds are blue”

EpistemologyAnalytic vs. synthetic propositions

Most analytic propositions are a prioriMost synthetic propositions are a posterioriAre a priori synthetic judgments possible?

Question posed by Kant; one of the most important questions in epistemology

Tautological propositionsIts constituent terms repeat themselves or they can be reduced to terms that do soThe proposition is, fundamentally, of the form a = aExample: He is old because he has lived many years, and he has lived many years because he is old No significant propositions can be derived from tautologiesTautologies are generally a priori, necessary, and analyticSignificant statements are generally a posteriori, contingent, and synthetic

EpistemologyAn epistemological fact: our perceptions somehow respond to presented facts so as to satisfy certain general conditions of responsiveness

To show how knowledge is possible, the philosopher epistemologist only speculates on the existence of the linkage between perceptions and factsScientists (e.g., perceptual and physiological psychologists) explain why perceptions respond to facts, describing the mechanisms for achieving responsivenessScientists (e.g., evolutionary psychologists) explain how the mechanism arose and was selected by Darwinian processes Thus philosophical and scientific activities differ

But the philosopher’s existential hypothesis may suggest experiments and investigations to the scientist A philosophical speculation may be sufficiently complete as to be amenable to an immediate empirical test

Ontology And MetaphysicsOntology: the theory of being as such, i.e., the basic characteristics of reality

Often taken as synonymous with metaphysics (the science of ultimate reality)

What is ultimately real versus merely apparent?

Examples: the real size of the moon versus its apparent size in the sky; the real color of an object versus its color viewed in dim light; the real structure of a desk (atoms, quarks, and empty space) versus its apparent structure (e.g., solid wood)Common sense is not a good guide to realityMetaphysicians do not agree on the nature of ultimate reality

ScienceSystemized knowledge derived from observation, study, and experimentationA branch of knowledge or study, especially one concerned with establishing and systemizing facts, principles, and methods, as by experiments and hypothesesAny system of knowledge that is concerned with the physical world and its phenomena and that entails unbiased observations and systematic experimentationA pursuit of knowledge covering general truths or the operation of fundamental lawsA skill based on systemized training (e.g., management science)Research: careful, systematic, patient study and investigation in some field of knowledge, undertaken to discover or establish facts or principles

Philosophy Of ScienceThe study of the scientific process or method and its validityIdentifies different styles of explanationcharacteristic of different sciences (e.g., psychology versus neurophysiology) or different stages in a given science (e.g., Newtonian versus Einsteinian theories of gravity) to determine how different explanatory stylesreflect the characteristic problems of different scientific fields and periods Central philosophical task: analyze clearly and explicitly

Standards by which scientists decide whether some interpretation is legitimate, justified, and conclusively establishedConsiderations that justify replacing a currently accepted interpretation (e.g., Newton’s theory of gravity) with a new alternative (e.g., Einstein’s theory of gravity)

From Data To EpiphaniesData: Unconnected numbers, names, dates, etc.Facts: Connected dataKnowledge: A particular assemblage of facts which can be taught and compressed; facts in context; actionable factsExperience: Primarily from self-directed interaction with the real world; internalizes knowledge and takes time to acquireShared visions: Philosophical and emotional collective understandings founded on our universality and not individuality; motivating force in organizations and gives purpose needed by leadersEpiphanies: Level of perception beyond logic and intuition; rare creative brilliance

From Data To Epiphanies

Data * Order = FactsFacts * Synthesis = KnowledgeKnowledge * Perspective = ExperienceExperience * Unifying Principles = Shared VisionShared Visions * Metalogic = Epiphanies

Section 2: Nature Of Normal Science

DefinitionsNormal science

Research based on one or more past scientific achievements, achievements that some particular scientific community acknowledges for a time as supplying the foundation for its further practice (Kuhn)

ParadigmA theory and body of knowledge sufficiently unprecedented and compelling as to attract an enduring group of adherents away from competing modes of scientific activity (Kuhn)A coherent tradition of scientific research, including law, theory, application, and instrumentation (Kuhn)A pattern, example, or model; an overall concept accepted by an intellectual community because of its success in explaining a complex process, idea, or set of data

Normal Science And ParadigmParadigms provide the framework for normal science

A common set of rules and standards for theory and researchMost researchers in a field share the paradigm – have a research consensusThe existence of a paradigm is a sign of a mature scienceResearch without a paradigm (e.g., in a new discipline) is open to new discovery – but chaotic so fact-gathering is nearly random; phenomena are described and interpreted in many different ways

The transformation of a paradigm – the transition from one paradigm to another – occurs in a scientific revolution

Some examples; discovery of: general relativity; plate tectonics; DNA; quanta and quarks; expansion of the universe; brain biochemicals; intelligent animal behavior; sulfur-based life cycles on sea floor vents; evolution through natural selection

Do the social sciences have paradigms yet?

ParadigmA framework for research and knowledge

Guides researchDetermines relative importance of data and factsServes as an idea filterA framework can be good or bad

Good: provides a common basis for discourse and research and the development of research tools; is an efficient mechanism for research and advancing knowledgeBad: no thinking “outside the box” – loss of creativity; facts not within the accepted paradigm are difficult to perceive or seen as irrelevant

A theory becomes a paradigm when it is generally accepted as superior to competing theories (i.e., explains and predicts phenomena and facts better)

ParadigmThe accepted paradigm need not be perfect and explain all facts and phenomena – just superior to alternative paradigms

An imperfect paradigm can explain phenomena satisfactorily and lead to better instruments, more accurate and precise measurements, and more facts and phenomena

As facts and phenomena become unexplainable by the paradigm and errors accumulate, a new paradigm emerges

Some researchers cling to the old paradigm as a new generation embraces the new paradigm –eventually the fogies fade away

The evolution (or revolution) of paradigms leads to an increasingly solid basis for the science

Researchers take the paradigm for granted and need not explain their research from first principles

This leads to less and less comprehension of the field by those outside it (because they are unfamiliar with the latest paradigm)

Normal ScienceThe (imperfect) paradigm requires further articulation and specification under “new or more stringent conditions.” (Kuhn)Normal science extends knowledge by

increasing the extent of the match between facts and the paradigm’s predictions and by further articulating phenomena, facts, and theories already explained by the paradigmNormal science is a type of “mopping-up” operation, gathering and refiningfacts and phenomena explained and predicted by the paradigmNormal science is not interested in seeking new phenomena (and, in any event, would not perceive new phenomena outside the paradigm “box”)

Normal ScienceNormal sciences focuses on:

Determining significant data and facts

The paradigm guides the search and perception of data & facts

Matching facts with theoryThe paradigm determines problems to be solved (and the instruments needed to solve problems)

Articulating theoryDetermination of physical constants(e.g., Avogadro’s number)Discovery of laws (e.g., Boyle’s law)

A paradigm may be a prerequisite for discovery of laws

Discovery of new ways of applying paradigm to new areas of interest

Normal ScienceTheoretical problems of normal science

Use “existing theory to predict factual information of intrinsic value” (Kuhn)

Examples: astronomical ephemerides; radio propagation curves; composition of human DNAOften relegated by scientists to engineers & technicians

Discover new application of paradigm or increase accuracy and precision of existing application

Normal science excludes novel concepts and phenomena

Novel problems are often rejected by the research community as metaphysicalNormal science is highly constrained and determined

Rules derive from paradigms, but “paradigms can guide research in the absence of rules”(Kuhn)

Section 3: Scientific Revolutions

Emergence Of Scientific DiscoveriesNormal science

Highly cumulative; steady increase in scope and precision of scientific knowledge

Discoveries (new facts) and inventions (new theories)

Lead to anomalies in normal scienceIncreasing anomalies lead to crises, which lead to a paradigm shift (replacement of an old paradigm with a new one)

“Crises are a necessary precondition for the emergence of novel theories”(Kuhn)

Once it has achieved the status of a paradigm, a scientific theory is declared invalid only if an alternative theory is available to take its placeCrisis loosens the rules of normal science “puzzle solving” to allow a new paradigm to emerge

Emergence Of Scientific DiscoveriesScientists rejecting one paradigm always, simultaneously, accept another

The process of paradigm rejection and acceptance involves comparing both paradigms with nature and each otherA scientist who rejects an accepted paradigm- the framework for the (current) normal science - without substituting a new paradigm, will be castigated and ostracized by his colleagues

Some anomalies are accepted as imperfections in normal science, while others generate crises and new paradigms

Some anomalies cause crises because of problems in:

Generalizing the paradigmApplying the paradigm to practical applicationsFurther development of the normal sciencewhich transforms a trivial anomaly into a significant anomaly (e.g., greater precision, more data, etc.)

Emergence Of Scientific DiscoveriesCrises begin with the blurring of a paradigm

Rules for normal science research are loosened, resembling research during pre-paradigm period

Transition from paradigm in crisis to new paradigm (from which a new tradition of normal science emerges):

Not a cumulative processThe field is reconstructed from new fundamentalsElementary theoretical generalizations change, along with methods and applicationsMuch time (e.g., one or two generations) can pass before awareness of breakdown of old paradigmand emergence or acceptance of new paradigm(e.g., more than 50 years to accept Newton’s laws after publication of Principia)

Resulting transition to new paradigm is scientific revolution

Scientific RevolutionsWhat are scientific revolutions and what is their function in scientific development?

Why should a change in paradigm be called a revolution?Scientific revolutions “seem revolutionary only to those whose paradigms are affected by them” (Kuhn). Outsiders perceive them as normal parts of the developmental process of science.

Scientific revolution: “Non-cumulativedevelopmental episodes in which an older paradigm is replaced in whole or part by an incompatible new one” (Kuhn).

Competing paradigms are incompatible –scientists must choose one or the otherSupporters of a paradigm argue in favor of it within the context of the paradigm – leading to circular arguments and tautology

Invention Of New TheoriesThree types of phenomena about which a new theory may be developed:

Phenomena already well-explained by existing paradigms

Rarely leads to new theoriesPhenomena whose nature is explained by existing paradigms but whose details can be understood only through further articulation of the theory

Rarely leads to new theoriesPhenomena with recognized anomalieswhich cannot be assimilated into existing paradigms

Often leads to new theoriesParadigms provide all phenomena –except anomalies – with a context in current theory and the scientist’s perception

Changes In The World ModelChanges in paradigms change the world model

Scientists adopt new instruments, look in new places for new phenomenaPerceptions change – familiar entities are seen in a different light and unfamiliar entities become noticeableThere is a change in the visual (and other senses) gestaltOld scientists who worked within the old paradigmmust learn the new gestalt (i.e., they need a perceptual transformation) – new scientists are immediately receptive and perceptiveWith different world models, old scientists and new scientists can see different things when looking at the same entitiesMany scientists cannot adapt and do not convertto the new paradigm (e.g., Kelvin never accepted electromagnetic theory)

Continue to believe older paradigm will eventually solve all the problems

Accepting The New ParadigmReasons for accepting a new paradigm

Objective reason: better ability to solve problems and make predictionsSubjective aesthetic reasons: simpler (e.g., Occam’s razor), neater, or more suitable explanations

Textbooks incorporate new paradigms and ignore the revolutions that produced them

Students take the pedagogically presentedparadigms for granted and do not understand the historical wrenching mental shifts needed to switch from older to newer paradigms Scientific progress is presented pedagogically as linear and cumulative, rather than as punctuated equilibrium (to borrow a term from a theory of evolution)

“Does a field make progress because it is a science, or is it a science because it makes progress?” (Kuhn)

Section 4: Philosophy Of Science

Laws Of ScienceLaws of science

Statements expressing observed repetitions or regularities as precisely as possible

Examples: fire is hot; ice is cold; a year is 365 daysUniversal law

A regularity observed at all times and placesExamples: all fire is hot; all ice is cold

Statistical lawA regularity occurs only in some percentage of cases

Examples: Ripe apples are red; a man’s life expectancy is 73 years

Empirical lawsBased on observable properties (e.g., color or length)

Theoretical lawsBased on non-observable properties or concepts (e.g., quanta)

Laws Of ScienceSingular statements

A single fact; an event in a single time and placeExample: I saw a brown and white collie at the corner of 5th and Maple Streets

Philosophy of science issueHow to go from singular statements to assertions of universal law

Science is based onDirect observation of single factsMany observations of single facts to discover regularitiesExpressing the regularities as laws

Laws Explain facts already knownPredict facts not yet known

Laws Of ScienceNo explanation (in science or everyday life) can be given without referring to at least one law

Fact explanations are really law explanations (where laws are tacitly assumed)Unless facts are connected with other facts by at least one law (explicitly stated or tacitly understood), they do not provide explanationsExample: Fact: “I am hungry.” Why are you hungry? Response: “I have not eaten all day.”

The response is an implicit universal law, not merely a fact: people who do not eat all day experience the sensation of hunger

A universal law may also be implicit in scientific explanations (as well as common sense explanations)

Laws Of ScienceStatistical laws

Because of ignorance (or, in the case of quantum theory, perhaps underlying reality) a statistical law may be used instead of the stronger universal lawExample: 5% of the people taking this medication will have an adverse side effect

Logic lawsLaws of logic are universal but say nothing about the real worldThey state relationships that hold between defined conceptsLogical statements cannot be contested (i.e., they are certainly true) because their truth is based on the meanings of the terms involved in the statements

Example: 1+2=3Cannot be used as a basis for scientific explanation because they cannot distinguish the actual universe from any other possible universe

Laws Of ScienceEmpirical laws

Are not certain like laws of logic – but they do reveal truths about our real worldBased on observed (through senses or instruments) phenomena

How vs. whyIn 19th century it was taught that scientistsshould only ask “how?” questions and not ”why?” questions – which could only have metaphysical answersNow the “why?” question is O.K. – the assumption is that the questioner requests an explanation in a framework of empirical laws

Explanations without laws are useless and meaningless

Examples: explanations for characteristics of life such as entelechy or the soul or a life force

Laws Of ScienceLaws predict as well as explain phenomena

Predict new facts not yet observedThe law may be statistical or universal

Example: there is a 75% chance of rain tomorrow

People use predictions based on laws in every act of human behavior that involves deliberate choice

Example: To stop the car you are driving you step on the brake because you know the universal law that stepping on the brake will stop the car (that the car will stop is a fact not yet observed)Example: You pour milk into the glass because you know the universal law that, on the earth, gravity causes the milk to fall downward into the glass (you would not do this while in orbit about the earth)

A general theory is a system of laws

InductionHow do we determine laws?

Laws constitute indirect knowledge –facts constitute direct knowledgeOn what basis are we justified in believing that a law holds?What justifies going from directly observed facts to generalized statements of law?

Known as the problem of induction

Deduction and inductionDeduction: goes from the general to the specific or singularInduction: goes from the singular to the generalThese definitions are an oversimplification and may be misleading

InductionDeductive logic

Inference leads from a set of premises to a conclusion as certain as the premisesIf premises are true, conclusion must be true

InductionThe truth of an of an inductive conclusion is never certain

Because the premises cannot be known with certainty

Even if the premises are assumed to be true and the inference is a valid inductive inference, the conclusion may be falseWith respect to a given set of premises, the most you can say is that the conclusion has a certain degree of probability

Inductive logic describes how to calculate the value of the probability

InductionIt is impossible to have a complete verification of a law – only a confirmation

Laws are based on a finite number of observations

Millions of positive observations are insufficient to verify a law

A law can be falsified by a single negative counter-instance

Although the negative counter-observation may itself be uncertain(e.g., because of error or deceit)

How many positive observationsare sufficient to confirm a law?

It is controversial whether quantitative values can be assigned to signify the strength of a law’s confirmation (e.g., based on many observations)

InductionClassical definition of probability

The ratio of the number of favorable cases to the number of all possible cases, given that all of the cases are equally probable

Involves counting casesExample: the probability of shooting a 2 with a fair die is 1/6 because all of the cases (numbers 1 to 6) are equally probableCriticized as circular definition because the word being defined – or a synonym like equipossible – appears in the definition

Another definition of probabilityA measurement of relative frequency

But no finite number of tests is sufficient for determining a probability with certainty

InductionBetter definition of probability

The limit of the relative frequency in an infinite series

With a sufficient number of observations, you can at least determine what the probability probably is

The probability of the probability may be calculatedThe only concept of probability acceptable in scienceCan be applied to prediction of single cases (e.g., the probability of rain for tomorrow) because the prediction is elliptical

Implicitly includes many previous observations (e.g., of weather conditions leading to observed instances of rain)

Another view of probabilityA probability statement is not a statement about the world but about a logical relation between two other statements

InductionLogical probability (or inductive probability)

A logical analysis of a stated hypothesis h and stated evidence e leads to the conclusion that h is not logically implied with certainty, but is partially implied to some degree (i.e., it is implied with a probability) The basic concept involved in all inductive reasoningInductive reasoning focused on evaluating this probability

Statistical probability in scienceNot purely logical – based on observed facts A scientific, empirical concept

Example: the probability of of medicine A curing disease Y is 0.73.

Logical probability is useful in meta-scientificstatements

Example: How trustworthy is the above probability prediction? What is the probability that the above probability is correct?

InductionThe degree of certainty or confidence that our beliefs can have about future events

Is logical probability, not statisticalprobability

Logical and statistical probability can be integrated

First premise is a statistical law (not a universal law)

Example: the relative frequency of brown shoes is 0.4

Second premise states that a certain individual has a certain property

Example: John owns four pairs of shoesThird statement asserts that this certain individual has a second property (i.e., this is the hypothesis based on the two premises)

Example: John owns one pair of brown shoes with a probability of 0.4

InductionBoth types of probability – statistical and logical – may occur in the same chain of reasoning

Statistical probability is part of the object language of scienceLogical probability (part of the meta-language of science) can be applied to statements about statistical probability

Indirect inductive inference is madeFrom a sample to the populationFrom a sample to an unknown future sampleFrom a sample to an unknown future instance (event or observation)

Inductive inference is madeFrom the population to a sample or instance

Experimental Method

All empirical knowledge depends on observing phenomena

Can observe passively (e.g., weather, stars, animals) and analyze observed phenomena(e.g., create taxonomies) – or even synthesize observed phenomena into lawsCan perform experiments

Some phenomena does not permit experiments (difficult or impossible or expensive or socially unacceptable), e.g., stellar evolution; spreading viruses on a subwayNeed quantitative concepts which can accurately measured

Experimental methodDetermine the relevant factors (variables) involved in the phenomena – ignore irrelevant factors (e.g., the weather in Phoenix has no affect on stellar evolution)

It can be difficult to distinguish relevant and irrelevant factors

Experimental MethodExperimental method (Continued)

Keep some of the selected relevant factors constant while varying the others

Quantify the relationships among subsets of variables and constantsExample: For a given gas at a constant temperature, volume is inversely proportional to pressure

Determine the relationships among all of the variables

Example: Type of gas; container size and shape; temperature; pressure; volume

Quantitative laws are superior to qualitative laws

Some quantitative laws can be derived from passive observationMany quantitative laws are derived from experimentation

Entity RelationshipsThree kinds of concepts defining relationships among entities (physical or conceptual objects): classification, comparison, and quantification

Classification (classificatory concept)Placing entities into a class; a taxonomyExamples: Things that are blue; trees; animals; circles; protons; quarksCan provide more or less information, e.g., the class of: animals, dogs, poodles, white poodles, miniature white poodlesProvides the least amount of informationof the three relationship conceptsThe relationships that we first learn as children, the names of things (e.g., that is a: house, cat, tree, cloud, paper, pencil, etc., etc.

Entity RelationshipsComparison (comparative concept)

Intermediate in information value (between classification and quantification)Describes relationships among entitiesExamples: A is taller than B; X is warmer than Y; C is heavier than D; P is more expensive than Q; etc.Allow for rank ordering (e.g., prioritizing) the entities in a setThe usefulness of comparisons often underestimated or ignored in science Comparisons can become basis for quantificationEntities in a domain can be arranged into a hierarchical structure (i.e., a stratified structure or quasi-serial arrangement) if the rules of symmetry (if a*b, then b*a) and transitivity (if a*b and b*c, then a*c) hold Comparative concepts (unlike class concepts) can generate complex structures of logical relationships

Entity RelationshipsQuantification (quantitative concept)

Difference between the qualitative and quantitative is not a difference in nature –it is a difference in our conceptual system (i.e., our language of discourse)Qualitative language: limited to predicates (e.g., the grass is green)Quantitative language: uses functorsymbols (i.e., symbols for functions that have numerical values)Two types of quantitative method: counting and measurementCounting is more basic than measuring – it is required for measuringCounting is actually an isomorphism, i.e., a one-to-one correlation between the event of pointing at (or touching) objects and the cardinal number of objects so determined

MeasurementProcedures are needed to be able describe the facts of nature by quantitative concepts (concepts with numerical values)

Counting gives values expressed in integersMeasurement gives values expressed in rational numbers (integers and fractions) and irrational numbers – allowing for mathematical tools such as calculus which make the scientific method more powerful

Need schema of rules for the process of measuringto give meaning to physical concepts (e.g., temperature)

Rule 1 (equality): if EM(a,b), then M(a) = M(b)Rule 2 (inequality): if LM(a,b), then M(a) < M(b)Rule 3 (base state): assign value (e.g., 0) to easily recognizable and reproducible state (i.e., standard)Rule 4 (rule of the unit): assign value to second reproducible stateRule 5 (difference equality scale): if EDM(a,b,c,d), then M(a) - M(b) = M(c) - M(d)

MeasurementThe ability to measure often leads to the quantitative concept

Example: the invention of the thermometer allowed the concept of temperature to be given a precise meaning

Extensive magnitudesMagnitudes in which two things can be joined to produce a new thing that is a combination of the values of the two physical or conceptual things (e.g., mass [physical] or time [conceptual])Examples: weight, length, volumeCan be measured with a 3-rule schema

Rule 1 (equality): if EM(a,b), then M(a) = M(b)Rule 2 (additivity): M(a*b) = M(a) + M(b)Rule 3 (unit rule): Specify the unit of value for the magnitude

But some extensive magnitudes are not additive(e.g., relativistic velocity, trigonometric functions [although angles are additive extensive magnitudes])

MeasurementAny defined standard (process) is acceptable for measurement

An arbitrary standard produces no logical contradictions – only complex or simple descriptions of the world Example: You may use your pulse as the time standard (instead of the frequency of the cesium atom or a pendulum)

When you exercise and your pulse rate increases, the earth’s rotation (and everything else in the universe) slows down; after you rest, the earth’s rotation speeds upYour pulse is as legitimate a time standard as a cesium atom – it just leads to a more complex description of the universe

Example: You may use a rubber ruler (which changes its length) as a standard of length instead of a metal ruler

It is a legitimate standard of length – it just leads to a more complex description of the universe

MeasurementA process version of Occam’s razorshould be used in selecting measurement standards

Occam’s (or Ockham’s) razor: a philosophical or scientific principle according to which the best explanation of an event is the one that is the simplest, using the fewest assumptions or hypotheses

The simplicity should reside in the description of the phenomena, not necessarily the measurement standard

Example: It is much simpler for me to use my pulse as a time standard than to design and build an atomic clock (or even an ordinary clock) – but the resulting description of phenomena would be extremely complexThe goal is to simplify the physical laws –even if it means employing complex measurement standards

MeasurementDerived magnitudes

Defined on the basis of primitive magnitudes(e.g., length, time, mass)Examples: density, velocity, acceleration

Are all entities and phenomena measurable?People assign numbers to nature (i.e., entities and phenomena in the universe) – the phenomena only provide observable qualitiesAll quantities except the cardinal numbers (which can be correlated to with discrete objects) are introduced by people when devising procedures for measurement – people devise rules on how numbers are to be assignedThus everything, in principle, can be measured

Albeit, quantum theory says that you may not be able to measure two things simultaneously (e.g., the position and velocity of an elementary particle)

MeasurementWhy do people apply numbers to natural phenomena?

Nature does not quantify (i.e., it is not natural)Quantification increases efficiency in describing phenomena (e.g., “it is 110 degrees” instead of “it is very very very very hot”)

The verbal description of colors is one exceptional phenomenon that has many (English) words to describe a multiplicity of states (quantified by electromagnetic frequencies and intensities) – most phenomena (e.g., temperature, mass, length) have very few verbal descriptors

Quantification permits the formation of quantitative lawswhich can explain phenomena and predict new phenomena

Some philosophers claim quantification does not convey as much of the reality of the phenomena as does natural language

But this is due to not understanding all of the informationcontained in the quantitative formulation (e.g., if you cannot read music, you will not perceive the music (in your mind) represented by the notes on a sheet of music)

Synthetic A PrioriIs it possible for knowledge to be both synthetic and a priori?

Immanuel Kant asked and answered the question (yes)Contemporary empiricists disagree with Kant (no)

Analytic knowledgeInvolves only the meaning relations of the termsLogical statementsExamples: “all dogs are animals” or “all fligneys are kwunkles”

Synthetic knowledgeInvolves knowledge of the worldFactual statements based on observation and experienceExamples: “all dogs need food and water to live” or “all mammals have hair”

Synthetic A PrioriA priori vs. a posteriori

Epistemological distinction between two kinds of knowledge

A priori knowledge (or statements)Independent of experienceBut not necessarily independent of genetic (evolutionary) experience and the cognitive (psychological) manifestation of genetic experienceAll analytic statements are a priori – it is never necessary to refer to experience as a justification for the truth of an analytic statement

Example: “all unicorns have a single horn”A posteriori knowledge (or statements)

Dependent on experience – empirical knowledgeCannot be justified without reference to experienceExamples: “sugar tastes sweet” or “ice is cold”

Synthetic A PrioriKant thought that (Euclidian) geometry was an example of knowledge that was synthetic and a priori (i.e., instinctively correct and yet true about the world)

But non-Euclidian geometry (which seems to be the geometry of the actual universe) was unknown at the timeMathematical geometry is analytical and a priori

Euclidean geometry says nothing about the real world

Physical geometry is synthetic and a posterioriNo geometry is both

There is no knowledge of any sort that is both a priori and synthetic (i.e., there is no example yet)

Theorems about reality are not certainTheorems that are certain are not about reality(i.e., insofar as they are a priori, they are not synthetic)

CausalityWhat is meant by “this is the cause of that”?

What does the cause-and-effect relation – that one event caused another event - mean?Example: I drop a plate on the floor and it shatters. What caused the plate to break?

Was it: Gravity causing the plate to accelerate to the floor? The hard floor disrupting the electrochemical bonds of the plate? The manufacturer (or shipper or retailer) who produced a microscopic fracture in the plate? Me because I released it from my hands? The flower pot that fell on my head causing me to release the plate from my hands? Etc.

Things do not cause events – processes cause events

The processes may be static (e.g., relevant variables or magnitudes are constant over time) or dynamicExample: a rock does not cause a window to break; complex physical processes between a thrown rock and the struck window cause the window to break

CausalityCausal relationships mean predictability

If (in principle) all relevant facts and laws are known about a state, then it is possible to predict, as a logical consequence, a subsequent state (said to be caused by the previous state)Predictability may be only a potential or possibility, not an actuality (e.g., if all the facts are not known at the time of the event)Many events have complex causes difficult to discernQuantum effects limit knowledge of causal relationshipsDavid Hume: causality is just a temporal succession of events

To investigate causality scientifically, it is necessary to isolate critical variables (i.e., examine one variable while holding all others constant)

This is very difficult to accomplish – especially with complex systems, such as organisms and social systemsExample: difficult to determine what causes or cures diseases

Causality And NecessityDoes causality imply necessity?

I.e., at any time or place, if a system is in a certain state then another specific state will followA law implies that the second state must follow, that there is a necessary connection between the two states

Example: if you increase the pressure on a gas, under constant temperature, it volume will decrease

Laws of logic hold under all conditions – any necessity then also always holds

If so defined: “if A, then B” always holdsBut laws of nature (science) hold only as a reflection of reality

A casual statement only describes a regularity of nature

Causality cannot be established on the basis of observing one case

It must be established on the basis of a general lawbased on many observations (e.g., life experiences)

Causality And NecessityDoes causality imply necessity?

In the regularities of nature called the laws of nature, causality does not imply necessityA law of nature asserting that a regularity holds for all time and place, must always be tentative

A single counter-observation, made at any time in the future, may determine the law to be wrong

Must cause and effect be of comparable magnitude (i.e., must cause equal effect)?

A claim used by creationists – the complexities of life (major effect) cannot be due to evolution (minor cause) But minor causes can always have major effects (e.g., a single photon can be used to trigger a thousand hydrogen bombs; a single sperm out of millions enters a specific egg and forms a Newton, an Einstein, an Edison, or a Hitler)

Determinism And Free WillCausal laws

Events can be predicted and explained on the basis of other eventsTotality of causal laws describes the causal structure of the world

DeterminismBelief in a strong causal structureGiven a complete description of the state of the universe at one instant and all relevant laws, any state (event) in the past or future of the universe can be calculatedQuantum mechanics has a causal structure that is probabilistic, not deterministic

Do people have free will (the ability to choose among alternatives) or is the feeling of having freedom of choice a delusion?

Determinism And Free WillOne view:

Even if determinism were true in the strong sense, a person would have free will if a choice (an action) originates from within the person’s character in accordance with the laws of psychology, i.e., the choice is made without external compulsion Example: choose to go bowling instead of the opera; choose to drink a glass of water instead of coffeeCausal regularity (deterministic or probabilistic) is necessary for free will

To make a choice, the consequences of the choice must be foreseen (at least probabilistically), which is not possible without causal regularity (e.g., a glass of water will slake my thirst better at this time than coffee -which judgment I base on previous actions)

Determinism And Free WillIssues with the view that a person has free will if a choice originates from within the person’s character in accordance with the laws of psychology, i.e., the choice is made without external compulsion

In principle, can you determine a person’s psychology and the laws of psychology?Is my need to work digging in the coal mine, so that I can earn money to get food to eat, an external compulsion or a free choice?If I go to the opera, instead of a football game, to avoid a conflict with my wife – is that external compulsion or free will?If I have a biochemical imbalance due to genetics (e.g., obsessive-compulsive disorder) or a temporary condition due to a psychological disturbance (e.g., road rage), is my choice to wash my hands repeatedly or commit a violent act made with or without compulsion?Does addiction to smoking involve free will or external compulsion?Is it possible to always distinguish between external and internal compulsion – and why should internal compulsion imply free will?